The monomial expansion formula for Hall-Littlewood $P$-polynomials

TL;DR

This paper presents a Hecke algebra-based derivation of Macdonald's expansion formula for Hall-Littlewood polynomials, generalizing Klostermann's recursions and providing a new algebraic perspective on these symmetric functions.

Contribution

It introduces a Hecke algebra approach to derive Macdonald's expansion formula, extending previous recursions and deepening the algebraic understanding of Hall-Littlewood polynomials.

Findings

Hecke algebra lift of expansion coefficients derived

Generalization of Klostermann's recursions proved

New algebraic derivation of Macdonald's formula obtained

Abstract

We give a Hecke algebra derivation of Macdonald's expansion formula for Hall-Littlewood polynomials in terms of semistandard Young tableaux. This is accomplished by first obtaining a Hecke algebra lift of the expansion coefficients and then proving a generalization of Klostermann's recursions.